Turkish Journal of Physics
Scaling in Time Series from Coupled Map Lattices
DOI

Abstract
Coupled Map Lattices(CML)[1] have been introduced to model spatial and temporal complexity in spatially extended systems. We have studied timeseries from a single site on a onedimensional periodic lattice of diffusively coupled logistic maps f(x)=\mu x(1x), x_i(n+1)=(1\epsilon)f(x_i(n)) +\epsilon/2(f(x_{i1}(n) 2f(x_i(n))+f(x_{i+1}(n)) which we consider as a model for a highdimensional dynamic system. We find, i) for random initial conditions that x_i(n) obeys a unimodal distribution for small \mu, and exhibits a phase transition to a bimodal distribution at \mu_c=3, the same value as for the single map [2], with the long time behaviour being characterized by extremely sharp distributions, ii) An order parameter can be defined as \psi = \langle x_i(n_{\rm odd/even})  \overline{x_i} \rangle and is found to vary as \psi \propto (\mu \mu_c)^{1/2}, with the same exponent as for the single map, and this value is independent of \epsilon for \epsilon \simeq .5, iii) higher periods than four tend to get smeared; the onset of chaotic behaviour depends now on the initial conditions and typically occurs around \mu=3.6. iv) Band merging and rather large stable periodic windows are observed in the chaotic region, the positions of which again depend on the initial conditions (or, equivalently, on i). v) The symbolic (kneading) sequence [2] can be defined with respect to \overline{x}. Then, the approach to chaotic behaviour is signalled by intermittent bursts of outofsequence series.
First Page
150
Last Page
150
Recommended Citation
ÇIKCI, Sevgi and ERZAN, Ayşe (1997) "Scaling in Time Series from Coupled Map Lattices," Turkish Journal of Physics: Vol. 21: No. 1, Article 20. Available at: https://journals.tubitak.gov.tr/physics/vol21/iss1/20